Calculate the mle estimate for mean, Applied Statistics

Assignment Help:

Each section of the SAT test is supposed to be distributed normally with a mean of 500 and a standard deviation of 100. Suppose 5 students in a class took the SAT math test. They received the following scores: 400, 450, 575, 600, and 625.

(a) Assuming a normal distribution, write out the likelihood function for estimating the mean μ and standard deviation σ of the average class score.

(b) Calculate the MLE estimate for μ and the standard deviation (σ) for this class.

(c) What is the value of the log-likelihood function at this estimate?

(d) What is the least-squares estimate for μ and σ in your data? Are there any differences? Why or why not?

(e) Using a likelihood-ratio test, test whether the MLE estimates from the class are significantly different from the national mean of 500 and national standard deviation of 100.

(Hint: Start by plugging those values into your log-likelihood function. Remember you are testing two restrictions).


Related Discussions:- Calculate the mle estimate for mean

Determine the compressive force, The weight of the engine in kN is given in...

The weight of the engine in kN is given in P2 and is suspended from a vertical chain at A. A second chain round the engine is attached at A, with a spreader bar between B and C. Th

Use event rule ot estimates the claim, Make a decision about the given clai...

Make a decision about the given claim. Use only the rare event rule, and make subjective estimates to determine whether events are likely. For example, if the claim is that a coi

Compute the standard deviation, Let X, Y, and Z refer to the three random v...

Let X, Y, and Z refer to the three random variables. It is known that Var(X) = 4, Var(Y) = 9, and Var(Z) = 16. It is further known that E(X) = 1, E(Y) = 2, and E(Z) = 4. Furthermor

Option price binomial tree, Modify your formulas from (1) to compute the pr...

Modify your formulas from (1) to compute the price at time 0 of an American put option with the same contract speci cations in the binomial model. Report the price of the American

Using the asymptotic distribution test the hypothesis, You are interested i...

You are interested in testing the distance of two golf balls, Brand A and Brand B. You take a random sample of 100 golfers, each of whom hits Brand A once and Brand B once. Define

Determine relative frequency, A sample of college students and a separate s...

A sample of college students and a separate sample of adults aged 30-59 were surveyed regarding the amount of fruit they eat each day.  The results are shown in the histograms belo

Collaboration policy,  Each question, by default, should be solved INDIVID...

 Each question, by default, should be solved INDIVIDUALLY, unless marked as \collaborative". Questions marked as \collaborative" implies that for those questions you are encourage

Random sampling method, Random Sampling Method In this method the units...

Random Sampling Method In this method the units are selected in such a way that every item in the whole universe has an equal chance of being included. In the words of croxton

Geometric mean, Geometric Mean is defined as the n th root of the ...

Geometric Mean is defined as the n th root of the product of numbers to be averaged. The geometric mean of numbers X 1 , X 2 , X 3 .....X n is given as

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd